Find the derivative of \( \dfrac{x^n-a^n}{x-a}\) for some constant a.
Let f(x) \( \dfrac{x^n-a^n}{x-a}\)
\( f'(x)=\dfrac{d}{dx}(\dfrac{x^n-a^n}{x-a})\)
By quotient rule,
\(\dfrac{(x-a)(nx^{n-1}-0)-(x^n-a^n)}{(x-a)^2}\)
\(\dfrac{nx^n-anx^{n-1}-x^n+a^n}{(x-a)^2}\)
Differentiate with respect to x xn loga x
Differentiate with respect to x xn tan x
Differentiate with respect to x x2 ex log x
Differentiate with respect to x x3 ex
Differentiate with respect to x x3 sin x
